Multi-parameter Quantum Magnetometry with Spin States in coarsened measurement reference

TL;DR

This paper explores multi-parameter quantum magnetometry using spin states, demonstrating improved simultaneous estimation precision over independent methods, even with measurement imperfections like coarsened references.

Contribution

It derives a general expression for simultaneous estimation precision and analyzes the impact of measurement coarsening on estimation performance.

Findings

Simultaneous estimation outperforms independent estimation with perfect measurements.

Coarsened measurement references can reduce the advantage of simultaneous estimation.

Rotation around the y-axis maintains the superiority of simultaneous estimation despite imperfections.

Abstract

We investigate the simultaneous estimation of the intensity and the orientation of a magnetic field by the multi-parameter quantum Fisher information matrix. A general expression is achieved for the simultaneous estimation precision of the intensity and the orientation, which is better than the independent estimation precision for the given number of spin states. Moreover, we consider an imperfect measurement device, coarsened measurement reference. For the case of the measurement reference rotating around the $y-$axis randomly, the simultaneous estimation always performs better than the independent estimation. For all other cases, the simultaneous estimation precision will not perform better than the independent estimation when the coarsened degree is larger than a certain value.